In an electric power appliance capable of applying various skin formulations, including skin treatment formulations, to a selected skin area, such as the facial skin area of the body, the applicator tip which actually contacts the skin with the formulation has a relatively short life and hence requires replacement from time to time. Such an applicator tip must have a very soft forward portion to maintain comfortable contact with the user's skin when applying the formulation. A user who experiences discomfort will be unlikely to continue to use the appliance. The applicator tip must also be readily securable to and removable from a drive end of the appliance motor. The replaceable applicator tip must reliably couple with the motor drive end so as to withstand an oscillating action of the motor drive without resulting in substantial noise or lost motion. The applicator assembly shown and described herein accomplishes such desired objectives.